A193265 E.g.f. A(x) = G(x)/x where G(x) satisfies: G(G(G(x))) = 2*x*G'(x) - G(x).

1, 1, 6, 81, 1828, 59910, 2629800, 146775160, 10047085200, 821599116300, 78674552192800, 8684916065005620, 1091429676788178240, 154543476785542516360, 24445478524707259098240, 4288239906998845117572000, 829048705765475214447735040

Offset: 0

Author

Paul D. Hanna, Jul 20 2011

Keywords

• nonn

Examples

			E.g.f.: A(x) = 1 + x + 6*x^2/2! + 81*x^3/3! + 1828*x^4/4! + 59910*x^5/5! +...
Let G(x) = x*A(x), then:
G(G(G(x))) = x + 6*x^2/2! + 90*x^3/3! + 2268*x^4/4! + 82260*x^5/5! +...+ (2*n-1)*n*a(n-1)*x^n/n! +...
which equals 2*x*G'(x) - G(x) = x*A(x) + 2*x^2*A'(x).
		

Links

• Paul D. Hanna, Table of n, a(n) for n = 0..149

Crossrefs

Cf. A193264.

Programs

PARI

{a(n)=local(G=x);if(n<0,0,if(n<=1,1,G=x+sum(m=2,n,a(m-1)*x^m/(m-1)!)+x^2*O(x^n); n!*polcoeff(subst(G,x,subst(G,x,G))-2*x*G',n+1)/(2*n-2)))}

Formula

a(n) = A193264(n+1)/(n+1).